Conditional Dependency of Financial Series: An Application of Copulas

Abstract

We develop a new methodology that measures conditional dependency. We achieve this by using copula functions that link marginal distributions, here chosen to obey a GARCH-type model with time-varying skewness and kurtosis. We apply this model to daily returns of stock-market indices. We find strong evidence of persistence in dependency both for local currency and $ US denominated series. For European stock markets, we also find evidence that large simultaneous returns of either sign lead to higher subsequent dependency. We show that dependency changes through time, as well. For stock markets within Europe, dependency increased whereas it decreased since the mid 90s when involving the S&P 500 or the Nikkei. We also suggest extensions for conditional asset pricing models involving time variation of co-skewness and co-kurtosis.